This thesis contributes to the econometric literature in two ways. Firstly, it introduces a new multivariate count model that presents advances in several aspects. Our multivariate time series count model can deal with issues of discreteness, overdispersion (variance greater than the mean) and both cross- and serial correlation, all at the same time. We follow a fully parametric approach and specify a marginal distribution for the counts where, conditionally on past observations the means follow a vector autoregressive process (VAR). This enables to attain improved inference on coefficients of exogenous regressors relative to the static Poisson regression, while modelling the serial correlation in a flexible way. The method is also innovative in the use of copulas, which builds the dependence structure between variables with given marginal distributions. This makes it possible to model the contemporaneous correlation between individual series in a very flexible way. Secondly, this thesis introduces a new approach to estimate the multivariate reduced rank regressions when the normality assumption is not satisfied. We propose to use the copula tool to generate multivariate distributions and, we show that this method can be applied in multivariate settings.
In terms of financial literature, this thesis provides two contributions. Firstly, with our multivariate count model we analyze diverse market microstructure issues about the submission of different types of orders by traders on stock markets. With this model, we can fully take into account the interactions between submissions of the various types of orders, which represent an advantage with respect to univariate models such as the autoregressive conditional duration model. Secondly, it contributes to portfolio research proposing a new dynamic optimal portfolio allocation model in a Value-at-Risk setup. This model allows for time varying skewness and kurtosis of portfolio distributions and the model parameters are estimated by weighted maximum likelihood in an increasing window setup. This last property allows us to have more accurate portfolio recommendations in terms of the amount to invest in the risk-free interest rate and in the risky portfolio.